Frequency Domain Problem - Revision history

Meylan at 09:30, 28 April 2010

2010-04-28T09:30:43Z

← Older revision		Revision as of 09:30, 28 April 2010
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	can be written as		can be written as
	<center>		<center>
	<math>\Phi(x,y,z,t) = \phi(x,y,z) e^{i\omega t} \,</math>		<math>\Phi(x,y,z,t) = \phi(x,y,z) e^{-\mathrm{i}\omega t} \,</math>
	</center>		</center>
	where <math>\omega</math> is the real and <math>\phi(x,y,z)</math>		where <math>\omega</math> is the real and <math>\phi(x,y,z)</math>
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	can simply we replaced by multiplication by <math>i \omega</math> (this only works		can simply we replaced by multiplication by <math>i \omega</math> (this only works
	because of the linearity in time).		because of the linearity in time).
	Sometimes it is assumed that the exponential is ~~negative~~ (but this is not the convention used here.		Sometimes it is assumed that the exponential is positive(but this is not the convention used here.

	The problem is now said to be a frequency domain problem.		The problem is now said to be a frequency domain problem.

	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

Meylan at 08:34, 9 September 2009

2009-09-09T08:34:47Z

← Older revision		Revision as of 08:34, 9 September 2009
Line 12:		Line 12:
	can simply we replaced by multiplication by <math>i \omega</math> (this only works		can simply we replaced by multiplication by <math>i \omega</math> (this only works
	because of the linearity in time).		because of the linearity in time).
	Sometimes ~~(possibly more than half the time)~~		Sometimes it is assumed that the exponential is negative (but this is not the convention used here.
	it is assumed that the exponential is negative.

	The problem is now said to be a frequency domain problem.		The problem is now said to be a frequency domain problem.

	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

Meylan at 08:34, 9 September 2009

2009-09-09T08:34:13Z

← Older revision		Revision as of 08:34, 9 September 2009
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	{{complete pages}}		{{complete pages}}

	~~This~~ is ~~closely connected with the [~~[Fourier Transform ~~in Time~~]~~]. Essentially after this~~		It is standard in linear water wave theory to take a
	~~we are left with a problem~~ in ~~which all~~ time ~~dependence is proportional to~~		[http://en.wikipedia.org/wiki/Fourier_Transform Fourier Transform] in time and assume
	<center><math>\~~exp~~ (i\omega t)\,</math></center>		that the solution for the real velocity potential <math>\Phi(x,y,z,t)</math>
	and ~~the resultant problem~~ (~~for complex valued potential~~, ~~displacement~~, ~~etc.~~)		can be written as
	is ~~said to be in the frequency domain (as opposed to the time domain).~~		<center>
	~~In many practical applications this is the only solution required, i.e. engineers simply want~~		<math>\Phi(x,y,z,t) = \phi(x,y,z) e^{i\omega t} \,</math>
	~~a table of force as~~ a function ~~of frequency~~. ~~Often the dependence is taken as~~		</center>
	~~<center>~~<math>~~\exp (-~~i\omega ~~t)\,~~</math>~~</center>~~		where <math>\omega</math> is the real and <math>\phi(x,y,z)</math>
	~~but we will not use this convention~~ in ~~this wiki~~.		is a complex function. This means that any time derivative
			can simply we replaced by multiplication by <math>i \omega</math> (this only works
			because of the linearity in time).
			Sometimes (possibly more than half the time)
			it is assumed that the exponential is negative.

			The problem is now said to be a frequency domain problem.

	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

Meylan at 08:30, 9 September 2009

2009-09-09T08:30:49Z

← Older revision		Revision as of 08:30, 9 September 2009
Line 1:		Line 1:
			{{complete pages}}

	This is closely connected with the [[Fourier Transform in Time]]. Essentially after this		This is closely connected with the [[Fourier Transform in Time]]. Essentially after this
	we are left with a problem in which all time dependence is proportional to		we are left with a problem in which all time dependence is proportional to

Meylan at 23:45, 10 September 2008

2008-09-10T23:45:54Z

← Older revision		Revision as of 23:45, 10 September 2008
Line 1:		Line 1:
	This is closely connected with the [[Fourier Transform in Time]]. Essentially after this		This is closely connected with the [[Fourier Transform in Time]]. Essentially after this
	we are left with a problem in which all time dependence is proportional to		we are left with a problem in which all time dependence is proportional to
	<center><math>\exp (i\omega t)</math></center>		<center><math>\exp (i\omega t)\,</math></center>
	and the resultant problem (for complex valued potential, displacement, etc.)		and the resultant problem (for complex valued potential, displacement, etc.)
	is said to be in the frequency domain (as opposed to the time domain).		is said to be in the frequency domain (as opposed to the time domain).
	In many practical applications this is the only solution required, i.e. engineers simply want		In many practical applications this is the only solution required, i.e. engineers simply want
	a table of force as a function of frequency. Often the dependence is taken as		a table of force as a function of frequency. Often the dependence is taken as
	<center><math>\exp (-i\omega t)</math></center>		<center><math>\exp (-i\omega t)\,</math></center>
			but we will not use this convention in this wiki.

	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

Meylan at 23:45, 10 September 2008

2008-09-10T23:45:02Z

← Older revision		Revision as of 23:45, 10 September 2008
Line 1:		Line 1:
	This is closely connected with the [[Fourier Transform in Time]]. Essentially after this		This is closely connected with the [[Fourier Transform in Time]]. Essentially after this
	we are left with a problem in which all time dependence is proportional to <math>\exp (i\omega t)</math>		we are left with a problem in which all time dependence is proportional to
			<center><math>\exp (i\omega t)</math></center>
	and the resultant problem (for complex valued potential, displacement, etc.)		and the resultant problem (for complex valued potential, displacement, etc.)
	is said to be in the frequency domain (as opposed to the time domain).		is said to be in the frequency domain (as opposed to the time domain).
	In many practical applications this is the only solution required, i.e. engineers simply want		In many practical applications this is the only solution required, i.e. engineers simply want
	a table of force as a function of frequency. Often the dependence is taken as		a table of force as a function of frequency. Often the dependence is taken as
	<math>\exp (-i\omega t)</math>		<center><math>\exp (-i\omega t)</math></center>

	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

Adi Kurniawan at 05:59, 22 August 2008

2008-08-22T05:59:11Z

← Older revision		Revision as of 05:59, 22 August 2008
Line 1:		Line 1:
	This is closely connected with the [[Fourier Transform in Time]]. Essentially after this		This is closely connected with the [[Fourier Transform in Time]]. Essentially after this
	we are left we a problem in which all time dependence is proportional to <math>\exp (i\omega t)</math>		we are left with a problem in which all time dependence is proportional to <math>\exp (i\omega t)</math>
	and the resultant problem (for complex valued potential, displacement etc.)		and the resultant problem (for complex valued potential, displacement, etc.)
	is said to be in the frequency domain (as opposed to the time domain).		is said to be in the frequency domain (as opposed to the time domain).
	In many practical applications this is the only solution required. i.e. engineers simply want		In many practical applications this is the only solution required, i.e. engineers simply want
	a table of force as a function of frequency. Often the dependence is taken as		a table of force as a function of frequency. Often the dependence is taken as
	<math>\exp (-i\omega t)</math>		<math>\exp (-i\omega t)</math>

	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

Meylan at 22:55, 16 December 2006

2006-12-16T22:55:11Z

← Older revision		Revision as of 22:55, 16 December 2006
Line 1:		Line 1:
	This is closely connected with the [[Fourier Transform in Time]]. Essentially after this		This is closely connected with the [[Fourier Transform in Time]]. Essentially after this
	we are left we a problem in which all time dependence is proportional to <math>~~e^{~~i\omega t}</math>		we are left we a problem in which all time dependence is proportional to <math>\exp (i\omega t)</math>
	and the resultant problem (for complex valued potential, displacement etc.)		and the resultant problem (for complex valued potential, displacement etc.)
	is said to be in the frequency domain (as opposed to the time domain).		is said to be in the frequency domain (as opposed to the time domain).
	In many practical applications this is the only solution required. i.e. engineers simply want		In many practical applications this is the only solution required. i.e. engineers simply want
	a table of force as a function of frequency.		a table of force as a function of frequency. Often the dependence is taken as
			<math>\exp (-i\omega t)</math>

	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

Meylan at 00:45, 2 June 2006

2006-06-02T00:45:59Z

← Older revision		Revision as of 00:45, 2 June 2006
Line 5:		Line 5:
	In many practical applications this is the only solution required. i.e. engineers simply want		In many practical applications this is the only solution required. i.e. engineers simply want
	a table of force as a function of frequency.		a table of force as a function of frequency.

			[[Category:Linear Water-Wave Theory]]

Meylan at 20:12, 22 April 2006

2006-04-22T20:12:56Z

← Older revision		Revision as of 20:12, 22 April 2006
Line 1:		Line 1:
	This is closely connected with the [[Fourier Transform in Time]]. Essentially after this		This is closely connected with the [[Fourier Transform in Time]]. Essentially after this
	we are left we a problem in which all time dependence is		we are left we a problem in which all time dependence is proportional to <math>e^{i\omega t}</math>
			and the resultant problem (for complex valued potential, displacement etc.)
	<math>e^{i\omega t}</math>		is said to be in the frequency domain (as opposed to the time domain).

	and the resultant problem is said to be in the frequency domain (as opposed to the time ~~domian~~).
	In many practical applications this is the only solution required. i.e. engineers simply want		In many practical applications this is the only solution required. i.e. engineers simply want
	a table of force as a function of frequency.		a table of force as a function of frequency.